{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9.1. Finding the root of a mathematical function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.optimize as opt\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return np.cos(x) - x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x5bb5470>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dm7fcuCbrhsYKnwcAAADA+BG5gQnrzN07cu3JXXn2zKaazPvaff058tJVuXWl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\n7hzzPTU3N2vXrl0xnwsAAAAAqWh5tV23fORW0Ip+OEi3W3q4r1/H5Ua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      "text/plain": [
       "<matplotlib.figure.Figure at 0x5bb5470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5, 5, 1000)\n",
    "y = f(x)\n",
    "fig, ax = plt.subplots(1, 1, figsize=(5, 3))\n",
    "ax.axhline(0, color='k')\n",
    "ax.plot(x, y)\n",
    "ax.set_xlim(-5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.739"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt.bisect(f, -5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x5d04198>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dm7fcuCbrhsYKnwcAAADA+BG5gQnrzN07cu3JXXn2zKaazPvaff058tJVuXWl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\nAguHwxHXXC5XHHYCAAAAAIimUwtdmjkyT26zQvc75VqyqyHqswEASER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      "text/plain": [
       "<matplotlib.figure.Figure at 0x5d04198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(5, 3))\n",
    "ax.axhline(0, color='k')\n",
    "ax.plot(x, y)\n",
    "# The zorder argument is used to put\n",
    "# the dot on top of the other elements.\n",
    "ax.scatter([_], [0], c='r', s=100,\n",
    "           zorder=10)\n",
    "ax.set_xlim(-5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.739"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "opt.brentq(f, -5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34.5 µs ± 855 ns per loop (mean ± std. dev. of 7 runs,\n",
      "    10000 loops each)\n",
      "7.71 µs ± 170 ns per loop (mean ± std. dev. of 7 runs,\n",
      "    100000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit opt.bisect(f, -5, 5)\n",
    "%timeit opt.brentq(f, -5, 5)"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}
